Using double opt-in helps you keep your email lists "cleaner" by making sure the emails you are putting on your lists are actually verified & are being used by the people submitting your forms.
When you select the list(s) that you want to add contacts to from a form, you will see a button that allows you to enable double opt-in.
This will send an email automatically to the email address the contact has entered, where the user has to click on a button in order to verify and actually be added as a subscriber.
Note: The Enable Double Opt-In Button will only appear once you have already selected the list that you want to send contact submissions to. It will be hidden until then.